metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20⋊7Q16, Q8.2D20, C42.60D10, (C4×Q8).8D5, C4⋊3(C5⋊Q16), C5⋊3(C4⋊2Q16), C20.22(C2×D4), (C2×C20).68D4, C4.18(C2×D20), (C5×Q8).19D4, (Q8×C20).9C2, C4⋊C4.257D10, C10.36(C2×Q16), C20⋊3C8.19C2, C4.14(C4○D20), C20.64(C4○D4), (C2×Q8).164D10, C20⋊2Q8.16C2, C2.17(C20⋊7D4), C10.69(C4⋊D4), (C4×C20).102C22, (C2×C20).351C23, C10.Q16.11C2, (Q8×C10).199C22, C2.10(D4.9D10), C10.112(C8.C22), (C2×Dic10).106C22, C2.7(C2×C5⋊Q16), (C2×C5⋊Q16).5C2, (C2×C10).482(C2×D4), (C2×C4).250(C5⋊D4), (C5×C4⋊C4).288C22, (C2×C4).451(C22×D5), C22.157(C2×C5⋊D4), (C2×C5⋊2C8).104C22, SmallGroup(320,658)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20⋊7Q16
G = < a,b,c | a20=b8=1, c2=b4, bab-1=a-1, ac=ca, cbc-1=b-1 >
Subgroups: 358 in 108 conjugacy classes, 47 normal (31 characteristic)
C1, C2, C4, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, Q8, C10, C42, C42, C4⋊C4, C4⋊C4, C2×C8, Q16, C2×Q8, C2×Q8, Dic5, C20, C20, C20, C2×C10, Q8⋊C4, C4⋊C8, C4×Q8, C4⋊Q8, C2×Q16, C5⋊2C8, Dic10, C2×Dic5, C2×C20, C2×C20, C5×Q8, C5×Q8, C4⋊2Q16, C2×C5⋊2C8, C4⋊Dic5, C5⋊Q16, C4×C20, C4×C20, C5×C4⋊C4, C5×C4⋊C4, C2×Dic10, Q8×C10, C20⋊3C8, C10.Q16, C20⋊2Q8, C2×C5⋊Q16, Q8×C20, C20⋊7Q16
Quotients: C1, C2, C22, D4, C23, D5, Q16, C2×D4, C4○D4, D10, C4⋊D4, C2×Q16, C8.C22, D20, C5⋊D4, C22×D5, C4⋊2Q16, C5⋊Q16, C2×D20, C4○D20, C2×C5⋊D4, C20⋊7D4, C2×C5⋊Q16, D4.9D10, C20⋊7Q16
►Regular action on 320 points
Generators in S320
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)(21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60)(61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100)(101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180)(181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220)(221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260)(261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280)(281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300)(301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320)
(1 108 193 253 168 60 320 36)(2 107 194 252 169 59 301 35)(3 106 195 251 170 58 302 34)(4 105 196 250 171 57 303 33)(5 104 197 249 172 56 304 32)(6 103 198 248 173 55 305 31)(7 102 199 247 174 54 306 30)(8 101 200 246 175 53 307 29)(9 120 181 245 176 52 308 28)(10 119 182 244 177 51 309 27)(11 118 183 243 178 50 310 26)(12 117 184 242 179 49 311 25)(13 116 185 241 180 48 312 24)(14 115 186 260 161 47 313 23)(15 114 187 259 162 46 314 22)(16 113 188 258 163 45 315 21)(17 112 189 257 164 44 316 40)(18 111 190 256 165 43 317 39)(19 110 191 255 166 42 318 38)(20 109 192 254 167 41 319 37)(61 294 129 268 151 85 212 224)(62 293 130 267 152 84 213 223)(63 292 131 266 153 83 214 222)(64 291 132 265 154 82 215 221)(65 290 133 264 155 81 216 240)(66 289 134 263 156 100 217 239)(67 288 135 262 157 99 218 238)(68 287 136 261 158 98 219 237)(69 286 137 280 159 97 220 236)(70 285 138 279 160 96 201 235)(71 284 139 278 141 95 202 234)(72 283 140 277 142 94 203 233)(73 282 121 276 143 93 204 232)(74 281 122 275 144 92 205 231)(75 300 123 274 145 91 206 230)(76 299 124 273 146 90 207 229)(77 298 125 272 147 89 208 228)(78 297 126 271 148 88 209 227)(79 296 127 270 149 87 210 226)(80 295 128 269 150 86 211 225)
(1 207 168 124)(2 208 169 125)(3 209 170 126)(4 210 171 127)(5 211 172 128)(6 212 173 129)(7 213 174 130)(8 214 175 131)(9 215 176 132)(10 216 177 133)(11 217 178 134)(12 218 179 135)(13 219 180 136)(14 220 161 137)(15 201 162 138)(16 202 163 139)(17 203 164 140)(18 204 165 121)(19 205 166 122)(20 206 167 123)(21 234 258 278)(22 235 259 279)(23 236 260 280)(24 237 241 261)(25 238 242 262)(26 239 243 263)(27 240 244 264)(28 221 245 265)(29 222 246 266)(30 223 247 267)(31 224 248 268)(32 225 249 269)(33 226 250 270)(34 227 251 271)(35 228 252 272)(36 229 253 273)(37 230 254 274)(38 231 255 275)(39 232 256 276)(40 233 257 277)(41 300 109 91)(42 281 110 92)(43 282 111 93)(44 283 112 94)(45 284 113 95)(46 285 114 96)(47 286 115 97)(48 287 116 98)(49 288 117 99)(50 289 118 100)(51 290 119 81)(52 291 120 82)(53 292 101 83)(54 293 102 84)(55 294 103 85)(56 295 104 86)(57 296 105 87)(58 297 106 88)(59 298 107 89)(60 299 108 90)(61 198 151 305)(62 199 152 306)(63 200 153 307)(64 181 154 308)(65 182 155 309)(66 183 156 310)(67 184 157 311)(68 185 158 312)(69 186 159 313)(70 187 160 314)(71 188 141 315)(72 189 142 316)(73 190 143 317)(74 191 144 318)(75 192 145 319)(76 193 146 320)(77 194 147 301)(78 195 148 302)(79 196 149 303)(80 197 150 304)
G:=sub<Sym(320)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220)(221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260)(261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320), (1,108,193,253,168,60,320,36)(2,107,194,252,169,59,301,35)(3,106,195,251,170,58,302,34)(4,105,196,250,171,57,303,33)(5,104,197,249,172,56,304,32)(6,103,198,248,173,55,305,31)(7,102,199,247,174,54,306,30)(8,101,200,246,175,53,307,29)(9,120,181,245,176,52,308,28)(10,119,182,244,177,51,309,27)(11,118,183,243,178,50,310,26)(12,117,184,242,179,49,311,25)(13,116,185,241,180,48,312,24)(14,115,186,260,161,47,313,23)(15,114,187,259,162,46,314,22)(16,113,188,258,163,45,315,21)(17,112,189,257,164,44,316,40)(18,111,190,256,165,43,317,39)(19,110,191,255,166,42,318,38)(20,109,192,254,167,41,319,37)(61,294,129,268,151,85,212,224)(62,293,130,267,152,84,213,223)(63,292,131,266,153,83,214,222)(64,291,132,265,154,82,215,221)(65,290,133,264,155,81,216,240)(66,289,134,263,156,100,217,239)(67,288,135,262,157,99,218,238)(68,287,136,261,158,98,219,237)(69,286,137,280,159,97,220,236)(70,285,138,279,160,96,201,235)(71,284,139,278,141,95,202,234)(72,283,140,277,142,94,203,233)(73,282,121,276,143,93,204,232)(74,281,122,275,144,92,205,231)(75,300,123,274,145,91,206,230)(76,299,124,273,146,90,207,229)(77,298,125,272,147,89,208,228)(78,297,126,271,148,88,209,227)(79,296,127,270,149,87,210,226)(80,295,128,269,150,86,211,225), (1,207,168,124)(2,208,169,125)(3,209,170,126)(4,210,171,127)(5,211,172,128)(6,212,173,129)(7,213,174,130)(8,214,175,131)(9,215,176,132)(10,216,177,133)(11,217,178,134)(12,218,179,135)(13,219,180,136)(14,220,161,137)(15,201,162,138)(16,202,163,139)(17,203,164,140)(18,204,165,121)(19,205,166,122)(20,206,167,123)(21,234,258,278)(22,235,259,279)(23,236,260,280)(24,237,241,261)(25,238,242,262)(26,239,243,263)(27,240,244,264)(28,221,245,265)(29,222,246,266)(30,223,247,267)(31,224,248,268)(32,225,249,269)(33,226,250,270)(34,227,251,271)(35,228,252,272)(36,229,253,273)(37,230,254,274)(38,231,255,275)(39,232,256,276)(40,233,257,277)(41,300,109,91)(42,281,110,92)(43,282,111,93)(44,283,112,94)(45,284,113,95)(46,285,114,96)(47,286,115,97)(48,287,116,98)(49,288,117,99)(50,289,118,100)(51,290,119,81)(52,291,120,82)(53,292,101,83)(54,293,102,84)(55,294,103,85)(56,295,104,86)(57,296,105,87)(58,297,106,88)(59,298,107,89)(60,299,108,90)(61,198,151,305)(62,199,152,306)(63,200,153,307)(64,181,154,308)(65,182,155,309)(66,183,156,310)(67,184,157,311)(68,185,158,312)(69,186,159,313)(70,187,160,314)(71,188,141,315)(72,189,142,316)(73,190,143,317)(74,191,144,318)(75,192,145,319)(76,193,146,320)(77,194,147,301)(78,195,148,302)(79,196,149,303)(80,197,150,304)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220)(221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260)(261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320), (1,108,193,253,168,60,320,36)(2,107,194,252,169,59,301,35)(3,106,195,251,170,58,302,34)(4,105,196,250,171,57,303,33)(5,104,197,249,172,56,304,32)(6,103,198,248,173,55,305,31)(7,102,199,247,174,54,306,30)(8,101,200,246,175,53,307,29)(9,120,181,245,176,52,308,28)(10,119,182,244,177,51,309,27)(11,118,183,243,178,50,310,26)(12,117,184,242,179,49,311,25)(13,116,185,241,180,48,312,24)(14,115,186,260,161,47,313,23)(15,114,187,259,162,46,314,22)(16,113,188,258,163,45,315,21)(17,112,189,257,164,44,316,40)(18,111,190,256,165,43,317,39)(19,110,191,255,166,42,318,38)(20,109,192,254,167,41,319,37)(61,294,129,268,151,85,212,224)(62,293,130,267,152,84,213,223)(63,292,131,266,153,83,214,222)(64,291,132,265,154,82,215,221)(65,290,133,264,155,81,216,240)(66,289,134,263,156,100,217,239)(67,288,135,262,157,99,218,238)(68,287,136,261,158,98,219,237)(69,286,137,280,159,97,220,236)(70,285,138,279,160,96,201,235)(71,284,139,278,141,95,202,234)(72,283,140,277,142,94,203,233)(73,282,121,276,143,93,204,232)(74,281,122,275,144,92,205,231)(75,300,123,274,145,91,206,230)(76,299,124,273,146,90,207,229)(77,298,125,272,147,89,208,228)(78,297,126,271,148,88,209,227)(79,296,127,270,149,87,210,226)(80,295,128,269,150,86,211,225), (1,207,168,124)(2,208,169,125)(3,209,170,126)(4,210,171,127)(5,211,172,128)(6,212,173,129)(7,213,174,130)(8,214,175,131)(9,215,176,132)(10,216,177,133)(11,217,178,134)(12,218,179,135)(13,219,180,136)(14,220,161,137)(15,201,162,138)(16,202,163,139)(17,203,164,140)(18,204,165,121)(19,205,166,122)(20,206,167,123)(21,234,258,278)(22,235,259,279)(23,236,260,280)(24,237,241,261)(25,238,242,262)(26,239,243,263)(27,240,244,264)(28,221,245,265)(29,222,246,266)(30,223,247,267)(31,224,248,268)(32,225,249,269)(33,226,250,270)(34,227,251,271)(35,228,252,272)(36,229,253,273)(37,230,254,274)(38,231,255,275)(39,232,256,276)(40,233,257,277)(41,300,109,91)(42,281,110,92)(43,282,111,93)(44,283,112,94)(45,284,113,95)(46,285,114,96)(47,286,115,97)(48,287,116,98)(49,288,117,99)(50,289,118,100)(51,290,119,81)(52,291,120,82)(53,292,101,83)(54,293,102,84)(55,294,103,85)(56,295,104,86)(57,296,105,87)(58,297,106,88)(59,298,107,89)(60,299,108,90)(61,198,151,305)(62,199,152,306)(63,200,153,307)(64,181,154,308)(65,182,155,309)(66,183,156,310)(67,184,157,311)(68,185,158,312)(69,186,159,313)(70,187,160,314)(71,188,141,315)(72,189,142,316)(73,190,143,317)(74,191,144,318)(75,192,145,319)(76,193,146,320)(77,194,147,301)(78,195,148,302)(79,196,149,303)(80,197,150,304) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60),(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100),(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180),(181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220),(221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260),(261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280),(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300),(301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320)], [(1,108,193,253,168,60,320,36),(2,107,194,252,169,59,301,35),(3,106,195,251,170,58,302,34),(4,105,196,250,171,57,303,33),(5,104,197,249,172,56,304,32),(6,103,198,248,173,55,305,31),(7,102,199,247,174,54,306,30),(8,101,200,246,175,53,307,29),(9,120,181,245,176,52,308,28),(10,119,182,244,177,51,309,27),(11,118,183,243,178,50,310,26),(12,117,184,242,179,49,311,25),(13,116,185,241,180,48,312,24),(14,115,186,260,161,47,313,23),(15,114,187,259,162,46,314,22),(16,113,188,258,163,45,315,21),(17,112,189,257,164,44,316,40),(18,111,190,256,165,43,317,39),(19,110,191,255,166,42,318,38),(20,109,192,254,167,41,319,37),(61,294,129,268,151,85,212,224),(62,293,130,267,152,84,213,223),(63,292,131,266,153,83,214,222),(64,291,132,265,154,82,215,221),(65,290,133,264,155,81,216,240),(66,289,134,263,156,100,217,239),(67,288,135,262,157,99,218,238),(68,287,136,261,158,98,219,237),(69,286,137,280,159,97,220,236),(70,285,138,279,160,96,201,235),(71,284,139,278,141,95,202,234),(72,283,140,277,142,94,203,233),(73,282,121,276,143,93,204,232),(74,281,122,275,144,92,205,231),(75,300,123,274,145,91,206,230),(76,299,124,273,146,90,207,229),(77,298,125,272,147,89,208,228),(78,297,126,271,148,88,209,227),(79,296,127,270,149,87,210,226),(80,295,128,269,150,86,211,225)], [(1,207,168,124),(2,208,169,125),(3,209,170,126),(4,210,171,127),(5,211,172,128),(6,212,173,129),(7,213,174,130),(8,214,175,131),(9,215,176,132),(10,216,177,133),(11,217,178,134),(12,218,179,135),(13,219,180,136),(14,220,161,137),(15,201,162,138),(16,202,163,139),(17,203,164,140),(18,204,165,121),(19,205,166,122),(20,206,167,123),(21,234,258,278),(22,235,259,279),(23,236,260,280),(24,237,241,261),(25,238,242,262),(26,239,243,263),(27,240,244,264),(28,221,245,265),(29,222,246,266),(30,223,247,267),(31,224,248,268),(32,225,249,269),(33,226,250,270),(34,227,251,271),(35,228,252,272),(36,229,253,273),(37,230,254,274),(38,231,255,275),(39,232,256,276),(40,233,257,277),(41,300,109,91),(42,281,110,92),(43,282,111,93),(44,283,112,94),(45,284,113,95),(46,285,114,96),(47,286,115,97),(48,287,116,98),(49,288,117,99),(50,289,118,100),(51,290,119,81),(52,291,120,82),(53,292,101,83),(54,293,102,84),(55,294,103,85),(56,295,104,86),(57,296,105,87),(58,297,106,88),(59,298,107,89),(60,299,108,90),(61,198,151,305),(62,199,152,306),(63,200,153,307),(64,181,154,308),(65,182,155,309),(66,183,156,310),(67,184,157,311),(68,185,158,312),(69,186,159,313),(70,187,160,314),(71,188,141,315),(72,189,142,316),(73,190,143,317),(74,191,144,318),(75,192,145,319),(76,193,146,320),(77,194,147,301),(78,195,148,302),(79,196,149,303),(80,197,150,304)]])
59 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | 4K | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 20A | ··· | 20H | 20I | ··· | 20AF |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 40 | 40 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
59 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | Q16 | C4○D4 | D10 | D10 | D10 | C5⋊D4 | D20 | C4○D20 | C8.C22 | C5⋊Q16 | D4.9D10 |
| kernel | C20⋊7Q16 | C20⋊3C8 | C10.Q16 | C20⋊2Q8 | C2×C5⋊Q16 | Q8×C20 | C2×C20 | C5×Q8 | C4×Q8 | C20 | C20 | C42 | C4⋊C4 | C2×Q8 | C2×C4 | Q8 | C4 | C10 | C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 2 | 2 | 2 | 2 | 8 | 8 | 8 | 1 | 4 | 4 |
Matrix representation of C20⋊7Q16 ►in GL4(𝔽41) generated by
| 14 | 30 | 0 | 0 |
| 11 | 9 | 0 | 0 |
| 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 40 |
| 27 | 11 | 0 | 0 |
| 27 | 14 | 0 | 0 |
| 0 | 0 | 0 | 6 |
| 0 | 0 | 34 | 17 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 20 | 34 |
| 0 | 0 | 28 | 21 |
G:=sub<GL(4,GF(41))| [14,11,0,0,30,9,0,0,0,0,40,0,0,0,0,40],[27,27,0,0,11,14,0,0,0,0,0,34,0,0,6,17],[1,0,0,0,0,1,0,0,0,0,20,28,0,0,34,21] >;
C20⋊7Q16 in GAP, Magma, Sage, TeX
C_{20}\rtimes_7Q_{16} % in TeX
G:=Group("C20:7Q16"); // GroupNames label
G:=SmallGroup(320,658);
// by ID
G=gap.SmallGroup(320,658);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,120,254,184,1123,297,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=b^4,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations